【LittleXi】Counting prime numbers

【LittleXi】Counting prime numbers

topic description

Given an integer N, returns the number of all prime numbers less than a nonnegative integer N.
204. Count prime numbers
P3912 Number of prime numbers

problem solving ideas

Sieve of Eratosthenes

When calculating each number, mark the multiples of the prime number

# 8112ms
class Solution:
    def countPrimes(self, n: int) -> int:
        cnt=0
        f=[1]*n
        for i in range(2,n):
            if f[i]:
                cnt+=1
                j=1
                while i*j<n:
                    f[i*j]=0
                    j+=1
        return cnt

Euler sieve

Optimized version, when marking prime numbers, those that have been marked repeatedly will not be marked

#python版本超时
class Solution:
    def countPrimes(self, n: int) -> int:
        prime=[0]*(n+1)
        vis=[1]*n
        for i in range(2,n):
            if vis[i]:
                vis[i]=0
                prime[0]+=1
                prime[prime[0]]=i
            for j in range(1,prime[0]+1):
                if i*prime[j]>n:
                    break
                if i*prime[j]<n:
                    vis[i*prime[j]]=0
                if i%prime[j]==0:
                    break
        return prime[0]

//cpp版本272ms
class Solution {
    
    
public:
    int countPrimes(int n) {
    
    
        int vis[5000010] = {
    
     0 };
        int prime[5000010] = {
    
     0 };
        for (int i = 2; i < n; i++)
        {
    
    
            if (vis[i] == 0)
            {
    
    
                vis[i] = 1;
                prime[++prime[0]] = i;
            }
            for (int j = 1; prime[j] * i <= n &&j <= prime[0]; j++)
            {
    
    
                vis[i * prime[j]] = 1;
                if (i % prime[j]==0)
                    break;
            }           
        }
        return prime[0];
    }
};